Aircraft: A320
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Critical

Flight enroute experienced a rapid depressurization event while cruising at FL340. Aircraft was dispatched with System 1 Cabin Pressure Control System on MEL. Cabin climbed rapidly as System 2 failed. We immediately began Emergency Descent Procedure; declared emergency with ARTCC; and descended to 10000 ft MSL. Cabin climbed above 14;000 as we descended; triggering automatic deployment of passenger oxygen masks. We eventually controlled cabin with Manual Pressurization System; received priority handling into ZZZ1; and made normal landing. Arrived at gate with no injuries or reported concerns by any passengers to flight crew upon deplaning.Normally reliable Automatic Pressure Control System on the Airbus allows one of two systems to be dispatched inoperative. The remaining System 2 in this case failed while cruising at FL340. We immediately began descent; hoping to avoid cabin altitude exceeding 14;000 ft; which would automatically deploy passenger oxygen masks. We were unable to manually close outflow valve in time to avoid this; but eventually controlled cabin manually to make an uneventful; normal landing in ZZZ1. We were doing a ZZZ round trip out of ZZZ1. Picking up the aircraft in ZZZ1; it had a deferred #1 pressure controller. We looked up the MEL and complied with the crew procedure for both legs. On the leg from ZZZ to ZZZ1; we were cruising at FL340. The ride was not good so we requested and were cleared to FL320. After leveling; I (PF) was reviewing the arrival and the Captain (PM) was getting a new ATIS. Just as I notice something different; the captain told me to put on my O2 mask. I notice the cabin alt on the lower ECAM turning red. I put on the mask and the Captain said we needed lower. I rolled the altitude selector down on the FCU and pulled for an open descent. The Captain then took control of the aircraft. I called ATC and said we need lower. ATC initially gave us FL280; then asked how low we needed. I responded 10;000. ATC gave up 12;000; follow shortly by 10;000.During this time the captain continued the descent. He also selected manual mode on the pressure controller and was closing the outflow valve. I check my QRH for ECAM exceptions and immediate action items for a Press Control 1&2 fail. There were none; so I procedure to do the ECAM. I declared an emergency about half way through the descent. Leveling off at 10;000; we took our masks off. The Captain called the FA's and made an announcement to the passengers. I completed the ECAM; there were no follow up procedures in the QRH. We were able to control the cabin via manual control. After a discussion to make sure we were on the same page; I referenced the expanded ECAM book. We assessed the condition of the passengers through the lead FA. ACARS dispatch; and checked fuel. We elected to continue to destination at 10;000. We landed in ZZZ1 uneventfully. We were met by the FA supervisor and line Maintenance at the gate.The event occurred because of the failure of the #2 pressure controller with the #1 pressure controller deferred.While not a suggestion about preventing the event; actions for an emergency descent should be in the QRH like an evacuation. I just completed training on the AB and we only did one in initial. Also; the emergency descent isn't a physical action; like other maneuvers; but a list of items that must be completed. I believe I could have done a better job if I could have flipped over my QRH and followed a step by step checklist. Things were very hectic; understanding the situation; reacting; talking with oxygen masks on. Having a checklist would help calm the situation. A320 flight crew reported cabin depressurized when #2 cabin pressure controller failed after being dispatched with #1 cabin pressure controller inoperative.